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He helped popularize the visual calculus devised by Mamikon Mnatsakanian with whom he also wrote a number of papers, many of which appeared in the American Mathematical Monthly. Apostol also provided academic content for an acclaimed video lecture series on introductory physics, The Mechanical Universe .
Ximera is a massive open online course by Ohio State University on Coursera and YouTube. [1] The system was originally known as MOOCulus and Calculus One. [2] The course features over 25 hours of video and exercises. The instructor is Jim Fowler, an associate professor of mathematics at the Ohio State University. [3]
Calculus of variations is concerned with variations of functionals, which are small changes in the functional's value due to small changes in the function that is its argument. The first variation [ l ] is defined as the linear part of the change in the functional, and the second variation [ m ] is defined as the quadratic part.
Produced starting in 1982, the videos make heavy use of historical dramatizations and visual aids to explain physics concepts. The latter were state of the art at the time, incorporating almost eight hours of computer animation created by computer graphics pioneer Jim Blinn along with assistants Sylvie Rueff [3] and Tom Brown at the Jet Propulsion Laboratory.
MIT video lectures on Multivariable Calculus, Fall 2007; Multivariable Calculus: A free online textbook by George Cain and James Herod; Multivariable Calculus Online: A free online textbook by Jeff Knisley; Multivariable Calculus – A Very Quick Review, Prof. Blair Perot, University of Massachusetts Amherst
While a few of these were limited to chronological reading lists and discussion topics, a majority provided homework problems and exams (often with solutions) and lecture notes. Some courses also included interactive web demonstrations in Java, complete textbooks written by MIT professors, and streaming video lectures. As of May 2018, 100 ...
He is the author of a textbook on Tensor Calculus (2013) as well as an e-workbook on Linear Algebra. He has recorded hundreds of video lectures; several dozen on Tensors (in a video course which may accompany his textbook) as well as over a hundred shorter videos on linear algebra. Many of these are available on YouTube as well as other sites.
Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional Euclidean space, . [1] The term vector calculus is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration.
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